Abstract
Decision theory is the study of how choices are and should be made.in a variety of different contexts. Here we look at the topic from a formal-philosophical point of view with a focus on normative and conceptual issues. After considering the question of how decision problems should be framed, we look at the both the standard theories of chance under conditions of certainty, risk and uncertainty and some of the current debates about how uncertainty should be measured and how agents should respond to it.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
Notes
- 1.
The restriction to a finite number of states of the world is made for simplicity, but the expected value will still be well defined even if we drop it.
- 2.
What level of resources is justified will of course depend on what is at stake.
- 3.
Savage was perfectly aware of this objection and drew an important distinction between small-world and grand-world decision problems. But he never produced a theory which, to his own and others satisfaction, explained how to convert grand-world problems into small-world ones satisfying the two requirements.
- 4.
It should be noted that the assumption of Consequentialism does not rule out a role for non-consequentialist considerations, in particular in determining the composition of the set of options. For instance if some actions are not permissable because they would violate someone’s rights then they would be excluded from the option set. What it does assume is that such non-consequentialist considerations do not enter beyond this point.
- 5.
To be clear, it is the ontological doctrine just described that should be rejected, not the associated epistemological doctrine according to which knowledge of preferences ultimately rests on observations of choice. The latter, in contrast to the former, has much to recommend it.
- 6.
It is important to note that it’s essential to the possibility of an additive representation that no cross-locational comparisons are possible. For such comparisons would constrain the co-scaling of the u j and there would then be no guarantee that the permitted co-scaling allowed for an additive representation.
- 7.
- 8.
I take this term from Broome [10].
- 9.
Savage in fact introduces one further postulate necessary for the extension of the expected utility representation to infinite consequences sets. This final postulate is very much in the spirit of the Sure-thing principle and as it does not raise any additional conceptual issues, I will not state it here.
- 10.
Printed, along with Savage’s letter in reply, in Drèze [12, pp. 76–81].
- 11.
- 12.
- 13.
- 14.
See for instance [8].
References
Allais, M. (1953). Le comportement de l’homme rationnel devant le risque: critique des postulats et axiomes de l’école Amé ricaine. Econometrica, 21, 503–546.
Anscombe, F. J., & Aumann, R. J. (1963). A definition of subjective probability. Annals of Mathematical Statistics, 34, 199–205.
Arrow, K. J. (1963). Social choice and individual values (2nd ed.). New York: Wiley.
Bernouilli, D. (1954/1738). Exposition of a new theory on the measurement of risk (L. Sommer, Trans.). Econometrica, 22, 23–26.
Binmore, K. (2009). Rational decisions. Princeton: Princeton University Press.
Bolker, E. (1966). Functions resembling quotients of measures. Transactions of the American Mathematical Society, 124, 292–312.
Bradley, R. (2007). A unified Bayesian decision theory. Theory and Decision, 63, 233–263.
Bradley, R. (2016). Ellsberg’s paradox and the value of chances. Economics and Philosophy, 32(2), 231–248.
* Bradley, R. (2017). Decision theory with a human face. Cambridge: Cambridge University Press [Presents a theory of rationality for bounded agents under conditions of severe uncertainty].
Broome, J. (1991). Weighing goods. Cambridge, MA: Basil Blackwell.
Buchak, L. (2013). Risk and rationality. Oxford: Oxford University Press.
Dreze, J. (1987). Essays on economic decisions under uncertainty. Cambridge: Cambridge University Press.
* Ellsberg, D. (1961). Risk, ambiguity, and the savage axioms. Quarterly Journal of Economics, 75, 643–669 [A very influential early critical assesment of Savage’s theory].
Evren, O., & OK, E. (2011). On the multi-utility representation of preference relations. Journal of Mathematical Economics, 47, 554–563.
Gigerenzer, G., & Selten, R. (2002).Bounded rationality. Cambridge: MIT Press
Halpern, J. Y. (2001). Alternative semantics for unawareness. Games and Economic Behavior, 37, 321–339.
Herstein, I. N., & Milnor, J. (1953). An axiomatic approach to measurable utility. Econometrica, 21(2), 291–297.
* Jeffrey, R. C. (1983). The logic of decision (2nd ed.). Chicago: University of Chicago Press [An influential formulation of decision theory in terms of propositional attitudes].
* Joyce, J. M. (1999). The foundations of causal decision theory. Cambridge: Cambridge University Press [The most complete formulation and defence of causal decision theory].
Karni, E., & Mongin, P. (2000). On the determination of subjective probability by choice. Management Science, 46, 233–248.
Karni, E., Schmeidler, D., & Vind, K. (1983). On state-dependent preferences and subjective probabilities. Econometrica, 51, 1021–1031.
Klibanoff, P., Marinacci. M., & Mukerji, S. (2005) A smooth model of decision making under ambiguity. Econometrica, 73, 1849–1892.
Krantz, D., Luce, R. D., Suppes, P., & Tversky, A. (1971). The foundations of measurement. Volume 1. Additive and polynomial representations. New York: Academic.
* Kreps, D. M. (1988). Notes on the theory of choice. Boulder/London: Westview Press [Excellent advanced introduction to decision theory].
Lewis, D. (1981). Causal decision theory. Australasian Journal of Philosophy, 59, 5–30.
Lipman, B. (1998). Decision theory without logical omniscience: Toward an axiomatic framework for bounded rationality. Review of Economic Studies, 339–361.
* Ramsey, F. P. (1926). Truth and probability. In D. H. Mellor (Ed.), Philosophical papers. Cambridge: Cambridge University Press, 2008 [Classic essay on the foundations of subjective probability and expected utility].
Rubinstein, A. (1998). Modeling bounded rationality. Cambridge: MIT Press
* Savage, L. J. (1954/1972). The foundations of statistics (2nd ed.). New York: Dover [The most influential formulation of subjective expected utility theory].
* Sen, A. K. (1970). Collective choice and social welfare. San Francisco: Holden-Day [Classic textbook on choice functions and social choice].
Simon, H. (1955). A behavioral model of rational choice. Quarterly Journal of Economics, 69, 99–118.
Stalnaker, R. ([1972]/1981b). Letter to David Lewis. In W. Harper, R. Stalnaker, & G. Pearce (Eds.), Ifs: Conditionals, belief, decision, chance, and time (pp. 151–152). Dordrecht: Reidel.
Stefánsson, H. O., & Bradley, R. (2015). How valuable are chances? Philosophy of Science, 82(4), 602–625.
Stefánsson, H. O., & Bradley, R. (Forthcoming 2017). What is risk aversion? British Journal of Philosophy of Science.
* von Neumann, J., & Morgenstern, O. (1944). Theory of games and economic behaviour. Princeton: Princeton University Press [Classic formulation of expected utility theory].
Wakker, P. (2010). Prospect theory: For risk and uncertainty. Cambridge: Cambridge University Press.
Weirich, P. (2004). Realistic decision theory: Rules for nonideal agents in nonideal circumstances. New York: Oxford University Press
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer International Publishing AG, part of Springer Nature
About this chapter
Cite this chapter
Bradley, R. (2018). Decision Theory: A Formal Philosophical Introduction. In: Hansson, S., Hendricks, V. (eds) Introduction to Formal Philosophy. Springer Undergraduate Texts in Philosophy. Springer, Cham. https://doi.org/10.1007/978-3-319-77434-3_34
Download citation
DOI: https://doi.org/10.1007/978-3-319-77434-3_34
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-77433-6
Online ISBN: 978-3-319-77434-3
eBook Packages: Religion and PhilosophyPhilosophy and Religion (R0)